Optimized Lower Leg Injury Probability Curves From Postmortem Human Subject Tests Under Axial Impacts

Abstract

Objective: Derive optimum injury probability curves to describe human tolerance of the lower leg using parametric survival analysis.

Methods: The study reexamined lower leg postmortem human subjects (PMHS) data from a large group of specimens. Briefly, axial loading experiments were conducted by impacting the plantar surface of the foot. Both injury and noninjury tests were included in the testing process. They were identified by pre- and posttest radiographic images and detailed dissection following the impact test. Fractures included injuries to the calcaneus and distal tibia–fibula complex (including pylon), representing severities at the Abbreviated Injury Score (AIS) level 2+. For the statistical analysis, peak force was chosen as the main explanatory variable and the age was chosen as the covariable. Censoring statuses depended on experimental outcomes. Parameters from the parametric survival analysis were estimated using the maximum likelihood approach and the dfbetas statistic was used to identify overly influential samples. The best fit from the Weibull, log-normal, and log-logistic distributions was based on the Akaike information criterion. Plus and minus 95% confidence intervals were obtained for the optimum injury probability distribution. The relative sizes of the interval were determined at predetermined risk levels. Quality indices were described at each of the selected probability levels.

Results: The mean age, stature, and weight were 58.2 ± 15.1 years, 1.74 ± 0.08 m, and 74.9 ± 13.8 kg, respectively. Excluding all overly influential tests resulted in the tightest confidence intervals. The Weibull distribution was the most optimum function compared to the other 2 distributions. A majority of quality indices were in the good category for this optimum distribution when results were extracted for 25-, 45- and 65-year-olds at 5, 25, and 50% risk levels age groups for lower leg fracture. For 25, 45, and 65 years, peak forces were 8.1, 6.5, and 5.1 kN at 5% risk; 9.6, 7.7, and 6.1 kN at 25% risk; and 10.4, 8.3, and 6.6 kN at 50% risk, respectively.

Conclusions: This study derived axial loading-induced injury risk curves based on survival analysis using peak force and specimen age; adopting different censoring schemes; considering overly influential samples in the analysis; and assessing the quality of the distribution at discrete probability levels. Because procedures used in the present survival analysis are accepted by international automotive communities, current optimum human injury probability distributions can be used at all risk levels with more confidence in future crashworthiness applications for automotive and other disciplines.

Keywords::

• biomechanics
• fracture
• lower extremities
• probability distributions
• survival analysis
• Weibull distribution

Acknowledgment

The authors thank Audrey Petitjean from the CESAR, Nanterr, France.

Additional information

Funding

The study was supported in part by the National Center for Advancing Translational Sciences, National Institutes of Health, through Grant Number 8UL1TR000055 and VA Medical Research. This research was supported in part by Cooperative Agreement W81XWH-12-0041 and the Department of Neurosurgery. This material is the result of work supported with resources and the use of facilities at the Zablocki VA Medical Center, Milwaukee, Wisconsin and the Medical College of Wisconsin. All authors are part-time employees of the Zablocki VA Medical Center, Milwaukee, Wisconsin. Any views expressed in this article are those of the authors and not necessarily representative of the funding organizations.